8 Chapter One
The Ultimate Speed Limit
T
he earth and the other planets of the solar system seem to be natural products of the evolu-
tion of the sun. Since the sun is a rather ordinary star in other ways, it is not surprising that
other stars have been found to have planetary systems around them as well. Life developed here
on earth, and there is no known reason why it should not also have done so on some of these
planets. Can we expect ever to be able to visit them and meet our fellow citizens of the universe?
The trouble is that nearly all stars are very far away—thousands or millions of light-years away. (A
light-year, the distance light travels in a year, is 9.46 1015 m.) But if we can build a spacecraft
whose speed is thousands or millions of times greater than the speed of light c, such distances
would not be an obstacle.
Alas, a simple argument based on Einstein’s postulates shows that nothing can move faster
than c. Suppose you are in a spacecraft traveling at a constant speed relative to the earth that
is greater than c. As I watch from the earth, the lamps in the spacecraft suddenly go out. You
switch on a flashlight to find the fuse box at the front of the spacecraft and change the blown
fuse (Fig. 1.6a). The lamps go on again.
From the ground, though, I would see something quite different. To me, since your speed
is greater than c, the light from your flashlight illuminates the backof the spacecraft (Fig. 1.6b).
I can only conclude that the laws of physics are different in your inertial frame from what they
are in my inertial frame—which contradicts the principle of relativity. The only way to avoid
this contradiction is to assume that nothing can move faster than the speed of light. This as-
sumption has been tested experimentally many times and has always been found to be correct.
The speed of light cin relativity is always its value in free space of 3.00 108 m /s. In all ma-
terial media, such as air, water, or glass, light travels more slowly than this, and atomic particles
are able to move faster in such media than does light. When an electrically charged particle moves
through a transparent substance at a speed exceeding that of light in the substance, a cone of light
waves is emitted that corresponds to the bow wave produced by a ship moving through the water
faster than water waves do. These light waves are known as Cerenkov radiation and form the
basis of a method of determining the speeds of such particles. The minimum speed a particle must
have to emit Cerenkov radiation is cnin a medium whose index of refraction is n. Cerenkov ra-
diation is visible as a bluish glow when an intense beam of particles is involved.(a)(b)Figure 1.6A person switches on a flashlight in a spacecraft assumed to be moving relative to the earth
faster than light. (a) In the spacecraft frame, the light goes to the front of the spacecraft. (b) In the
earth frame, the light goes to the back of the spacecraft. Because observers in the spacecraft and on
the earth would see different events, the principle of relativity would be violated. The conclusion is
that the spacecraft cannot be moving faster than light relative to the earth (or relative to anything else).bei48482_ch01.qxd 1/15/02 1:21 AM Page 8